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waves2Foam Manual

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F
y z
∂ρu
∂t +∇ · ρuuT=−∇p+g·(xxr)ρ+∇ · µtot u
ρut
= (∂/∂x, ∂/∂y, ∂/∂z)pg
x= (x, y, z)xr
µtot
∇ · u= 0
p=pρg·xp
n
u=nup
up
(1 + Cm)
∂t
ρu
n+1
n∇ · ρ
nuuT=−∇p+g·(xxr)ρ+1
n∇ · µtotuFp
CmFp
F
∂F
∂t +∇ · uF+∇ · ur(1 F)F= 0
urF
ρ=F ρ1+ (1 F)ρ0µ=F µ1+ (1 F)µ0
F= 0
F= 1 F= 1 F= 0
F[0,1]
∂F
∂t +1
n(∇ · uF+∇ · ur(1 F)F) = 0
n
φ= (1 wR)φ+wRφ
wR[0,1]
αu
wR
˜wR= 1 (1 w
R)/max
w
R= 1 wR˜wR
max
wR(σ= 1) = 0 wR(σ= 0) = 1 σ
wR= 1 exp σp1
exp 1 1
p3.5
wR= 1 σp
p
p
wR=σ3+ 3˜σ2
˜σ= 1 σ
Fp
ρ=au+bukuk2
a b Cm
Cm=γp
1n
n
γp0.34
a b
a=α(1 n)3
n2
ν
d2
50
, b =β1n
n3
1
d50
ν d50
a b
a=α(1 n)2
n3
ν
d2
50
, b =β1 + 7.5
KC 1n
n3
1
d50
ν d50
α β KC
KC
3×3 = 9
1
0 1
σ
1
φ3
φρ
φF3
φ φF
φF
φ φρ
φρ= (ρF=1 ρF=0)φF+ρF=0 φ
φF
φF=φρρF=0φ
ρF=1 ρF=0
F= 1
F
q=X
f∈F
φF,f
Sf
kSfk2
q3Sf
φF
φFφ φρ
φF
q
Hm=H01 + sin 1
N(ωt k·x)
HmH0
N ω k
h/L h L
m
1
m m
1
η=
N
X
i
aicos(ωitki·x+ϕi)
η N ai
i ω kϕ
aiωi
ωiϕi
x0t0
0
t= 0
t= 0
x y z
x y z
t= 0
x
kω
k
kω
up
kω
KC
f= 1/Tef
Te
100
R(τ) = 1
m0Z−∞
0
S(f) cos 2πf τ f
R(τ)S(f)f τ
m0
Rd(τ)'1
2md,0
N1
X
n=0
[Sd(fn) cos(2πfnτ) + Sd(fn+1 ) cos(2πfn+1τ)] ∆fn
dfn=fn+1 fnN
η
η(t, x) =
N
X
m=1
amcos (ωmtkm·x+ϕm)
amωmkmx
ϕm[0,2π]
am=p[Sd(fm1) + Sd(fm)]∆fm1
ωm=π(fm+fm1)
τ > 0 cos(2π fnτ)=1
n TrTm01
Tr
fn=nδf0fn=δf0n= 0,1...,N
Tr=1
δf0
=N
fN
fN
N fNTr
fn= (1 + f)δf0
fn=nδf0+αfδf0nn+ 1
21=δf0(n+αfAn)
1/(1 N)< αfαf= 0
cos(2πfnτ) = cos(2πnδf0τ) cos(2παfAnδf0τ)
sin(2πnδf0τ) sin(2παfAnδf0τ)
n
nδf0τ=K αfAnδf0τ=L
K L τ
K
n
L
An
αf= 1
α
τ Rd= 1
αfTrα= 1/4Tr= 1/δf0Tr= 4/δf0
α= 4 αfδf0
δf0αf
Tr
S
fLfPfU
[fL, fP[
NL=fPfL
fUfP (N+ 1)
[fP, fU]NU=N+ 1 NL
fn=fL+ (fPfL) sin 2π
4NL
nn= 0,...NL1
fNL+n=fP+ (fUfP)1cos 2π
4NU
n n= 0,...NU
f f fL= 0.03
fU= 1.4Tp= 3 N= 200
N= 35
N
N= 200
N= 20
N
Tr'15 Tr
N|Rd|
Tr
0 0.2 0.4 0.6 0.8 1 1.2 1.4
f, [Hz]
10 -4
10 -3
10 -2
10 -1
f, [Hz]
A.
0.2 0.25 0.3 0.35 0.4 0.45 0.5
f, [Hz]
0
0.2
0.4
0.6
S, [m2s]
B.
Equidistant
Cosine stretching
f f
fL= 0.03 fU= 1.4Tp= 3 N= 200 N= 35
Hm0= 4m0Tm01 =m0/m1
Tm02 =pm0/m2Tm10 =m1/m0N
mii
mi=Z
0
fiS(f)f
N
N= 10,000
N= 10,000
N
N
t= 0.02 Te= 5,000
TrTr= 730 N= 1,000
N
N N = 100
0.1%
N= 100
0 20 40 60 80 100
-1
-0.5
0
0.5
1
η, [m]
A.
0 20 40 60 80 100
t, [s]
-1
-0.5
0
0.5
1
η, [m]
B.
0 10 20 30 40 50
-1
0
1
R, [-]
A.
0 100 200 300 400 500
t, [s]
-1
0
1
R, [-]
B.
σ σ
10 110 210 310 4
0.98
1
1.02
Rel. Hm0, [-]
A.
10 110 210 310 4
0.98
1
1.02
Rel. Tm01, [-]
B.
10 110 210 310 4
0.98
1
1.02
Rel. Tm02, [-]
C.
10 110 210 310 4
N, [-]
0.98
1
1.02
Rel. Tm10, [-]
D.
Equidistant
Cosine stretching
N
N= 10,000
η=η0+
N
X
n=1
ancos(ωntkn·x+φn)
η η0N ω
tk x φ
η=η0+
N
X
n=1
an[cos(ωnt+φn) cos kn·xsin(ωnt+φn) sin kn·x]
02468
10 -4
10 -2
10 0
Exceedance
Equidistant
N= 100
02468
10 -4
10 -2
10 0
Exceedance
N= 200
02468
10 -4
10 -2
10 0
Exceedance
N= 500
02468
(H/Hrms)2, (T /Tp)2, [-]
10 -4
10 -2
10 0
Exceedance
N= 1000
02468
10 -4
10 -2
10 0Cosine stretching
N= 100
02468
10 -4
10 -2
10 0
N= 200
02468
10 -4
10 -2
10 0
N= 500
02468
(H/Hrms)2, (T /Tp)2, [-]
10 -4
10 -2
10 0
N= 1000
Rayleigh
Wave height
Wave period
(H/Hrms )2(T/Tp)2
±σ
x
t
2N
z
t x y
x y z
(x, y)z
N= 1
N= 100
10 010 110 210 310 4
10 0
10 1
10 2
10 3
TN/TN=1, [-]
A.
Direct method
Split method
10 010 110 210 310 4
N, [-]
0
10
20
30
Direct over split, [-]
B.
N= 1
5
N= 100 N= 1,000
N2
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Conference Paper
Full-text available
A 2D RANS-VOF model is used to simulate the flow and sand transport for two different full-scale laboratory experiments: i) non-breaking waves over a horizontal sand bed (Schretlen et al., 2011) and ii) plunging breaking waves over a barred mobile bed profile (Van der Zanden et al., 2016). For the first time, the model is not only tested and validated in terms of water surface and outer flow hydrodynamics, but also in terms of wave boundary layer processes and sediment concentration patterns. It is shown that the model is capable of reproducing the outer flow (mean currents and turbulence patterns) as well as the spatial and temporal development of the wave boundary layer. The simulations of sediment concentration distributions across the breaking zone show the relevance of accounting for turbulence effects on computing suspended sediment pick-up from the bed.
Thesis
Full-text available
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Article
Full-text available
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